arXiv research

This research optimizes plate structures to reduce vibrations in vehicles and aircraft.

Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.

Sophie Germain's mean curvature deserves recognition as a surface shape measure.

The wave equation $u_{tt} = c^2 u_{xx}$ is generally regarded as a linear approximation to the equation describing the amplitude of a transversely vibrating elastic string in the plane. But, as is shown in \cite{BC96}, the assumption of transverse vibration in fact implies that the wave equation describes the vibration…

In Chinese societies, superstition is of paramount importance, and vehicle license plates with desirable numbers can fetch very high prices in auctions. Unlike other valuable items, license plates are not allocated an estimated price before auction. I propose that the task of predicting plate prices can be viewed as a …

The game of plates and olives, introduced by Nicolaescu, begins with an empty table. At each step either an empty plate is put down, an olive is put down on a plate, an olive is removed, an empty plate is removed, or the olives on two plates that both have olives on them are combined on one of the two plates, with the …

Transformer model predicts train axle vibrations for safer maintenance.

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…

Estimates for plate eigenvalues with nonzero Poisson's ratio.

This paper reviews traditional and modern methods for detecting structural damage using vibrations.

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…

The paper analyzes the stability of an observer error in a vibrating string system.

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine som…

Extends plate problems to differential forms on manifolds.

A novel ensemble classifier improves vibration-based quality monitoring accuracy.

In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter.

Un sous-système de dimension différentielle au plus 2 d'une extension plate est plate. Si un tel système plat est stationnaire, il admet des sorties plates indépendantes du temps. A subsystem of a flat system of differential dimension at most 2 is flat. Furthermore, if such a flat system is stationary, we show that the…

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a surface. Thi…

This work models variability in composite blades' vibrations.

For a bounded domain $Ω$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

Safe RL-based vibration control using LQR guidance.

PAVI speeds up Bayesian inference for large datasets.

New isoperimetric inequality for clamped plates in RCD(0,N) spaces, sharp and stable.

This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\sqrt {Γ_{k+1}-Γ_{1}}$ and $\sqrt {Γ_{k}-Γ_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap betwe…

The study focuses on the experiment of using three different smartphones to collect acceleration data from vibration for the road roughness detection. The Android operating system is used in the application. The study takes place on asphaltic pavement of the expressway system of Thailand, with 9 km distance. The run ve…

Study develops efficient algorithm for probabilistic penetration response of composite plates.

The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.

The study introduces a new stickiness parameter for stock prices using a non-linear model.

The paper studies eigenvalue inequalities for a clamped plate problem involving a generalized elliptic differential operator.

Proves Payne conjecture for buckling and membrane eigenvalues.

Study examines how body segments respond to random vibrations.

Paper predicts bearing degradation stages for pharmaceutical industry maintenance.

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The…

We study the conformal plate buckling equation (Laplace--Beltrami)^2 u =1, where the L-B operator is for the metric g = e^{2u}g_0, with $g_0$ the standard Euclidean metric on R^2. This conformal elliptic PDE of fourth order is equivalent to the nonlinear system of elliptic PDEs of second order, Delta u +K_g e^(2u)=0, D…

We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

Develops control and observer methods for complex systems.

PAVI speeds up VI for large-scale studies by sharing parameterization across i.i.d. variables.

New metric tensor field on symmetric matrices simplifies eigenvector computation.

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a …

We study Lord Rayleigh's problem for clamped plates on an arbitrary $n$-dimensional $(n\geq 2)$ Cartan-Hadamard manifold $(M,g)$ with sectional curvature $\textbf{K}\leq -κ^2$ for some $κ\geq 0.$ We first prove a McKean-type spectral gap estimate, i.e. the fundamental tone of any domain in $(M,g)$ is universally bounde…

This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.

This work develops a high precision fault diagnosis classifier using XAI insights.

Shells resist three out of six possible loads if simply connected.

Sample size determination for a data set is an important statistical process for analyzing the data to an optimum level of accuracy and using minimum computational work. The applications of this process are credible in every domain which deals with large data sets and high computational work. This study uses Bayesian a…

Six AI solutions accurately detect growth plate planes in mice bone scans.